Lun Du, Zhicong Lu, Yun Wang, Guojie Song, Yiming Wang, Wei Chen

Network embedding is a method of learning a low-dimensional vector representation of network vertices under the condition of preserving different types of network properties. Previous studies mainly focus on preserving structural information of vertices at a particular scale, like neighbor information or community information, but cannot preserve the hierarchical community structure, which would enable the network to be easily analyzed at various scales. Inspired by the hierarchical structure of galaxies, we propose the Galaxy Network Embedding (GNE) model, which formulates an optimization problem with spherical constraints to describe the hierarchical community structure preserving network embedding. More specifically, we present an approach of embedding communities into a low dimensional spherical surface, the center of which represents the parent community they belong to. Our experiments reveal that the representations from GNE preserve the hierarchical community structure and show advantages in several applications such as vertex multi-class classification and network visualization. The source code of GNE is available online.